Surprisingly, fixation functions were observed to increase under cases where mutants did relatively worse among residents than among themselves for large populations. This was observed under 3 game orderings, where fixation probabilities increased for small populations but eventually decreased to infinity. It was already noted in [1]} that payoffs \(b\)  and \(c\)  are the only relevant entries of the payoff matrix under \(N=2\) . Thus, under small populations, increasing population size means increasing the maximum frequency of individuals of the same type that are found in the population before fixation occurs (e.g. \(0\%\)  for \(N=2\) , \(50\%\)  for \(N=3\) , \(80\%\)  for \(N=6\) ). Increasing population size thus increases the frequency of interactions between equal types. Having high enough \(a>\lambda -b\)  and low enough \(d<c\)  allowed for fixation probabilities to increase for the smallest population sizes, even when \(d/b>c/a\) .
